Question

A Ferris wheel completes one revolution every 90 s. The cars reach a
maximum of 55 m above the ground and a minimum of 5 m above the ground.
The height, h, in metres, above the ground can be modeled using a sine function,
where t represents time, in seconds. Assume ride starts when you get on the ride.
a) Draw a sketch showing one rotation of the Ferris wheel.
b) Determine an equation that models the height of a rider.
c) Determine the height of a rider after 70 seconds.

Answer 1

sin(kx) has period 2π/k, so since we have period 90, k = π/45

y = a sin(π/45 t+b)) + c

sin(x) has a minimum at t = 3π/2, and our ferris wheel has a minimum at t=0, so

y = a sin(π/45 t + 3π/2)) + c

The axle is at (55+5)/2 = 30, so

y = a sin(π/45 t + 3π/2) + 30

The amplitude is (55-5)/2 = 25, so

y = 25 sin(π/45 t + 3π/2)) + 30
or
y = 25 sin(π/45 (t + 135/2)) + 30